Η κατανομή του αριθμού των αποζημιώσεων μέχρι τη χρεοκοπία
Φλουρής, Κωνσταντίνος Ε.
SubjectΕταιρείες -- Πτώχευση ; Κατανομή (Οικονομική θεωρία) ; Συναρτήσεις ; Διαχείριση κινδύνου -- Οικονομετρικά μοντέλα ; Μισθοί και ημερομίσθια -- Οικονομετρικές μέθοδοι
A quantity of central interest in risk theory is the number of claims until ruin in a risk process. This is a defective random variable, which is closely related to the time of ruin. The present thesis studies the explicit expression of the probability function of the number of claims until ruin, on a theoretical basis, assuming that both claim-sizes and interarrival times are exponential. The main result is inspired by a recent paper in Frostig et al (2010). We give numerical examples for the defective distribution of the number of claims until ruin, as well as for the proper distribution of this random variable, given that ruin occurs. For the case that the distribution of the number of claims is a member of the (a,b,0) or the (a,b,1) class of distributions, we give explicit expressions for the mean and the variance. We also obtain an explicit expression for the coe_cient of skewness of the proper distribution of number of claims until ruin, given that ruin occurs, and therefore, we give a theorem for the skewness of this proper distribution. Moreover, we present two approximations for the distribution of number of claims until ruin, given that ruin occurs with a geometric distribution.